The president also told reporters he's "looking at" whether there are any actions that can be taken against the Times, which said it was taking an extraordinary step in allowing the piece to be published anonymously.
"I think it is national security".
"I think that if we're going to meet it's got to be a fair meeting", he said.
The president addressed a group of sheriffs gathered in the East Room shortly after the Times posted the piece.
In the piece, the writer had claimed: "The root of the problem is the president's amorality".
"It's very unfair to our country and to the millions of people that voted really for us", Mr. Trump said.
Mr Trump said it was an issue of "national security".
President Donald Trump's reaction was a combination of rage and self-pity.
A Justice Department spokeswoman said the department does not confirm or deny investigations.
While crediting the few successes Trump's White House has seen, the essay adds that "these successes have come despite - not because of - the president's leadership style, which is impetuous, adversarial, petty and ineffective".
In an interview Thursday with Fox News, Trump said the author "may not be a Republican, it may not be a conservative, it may be a deep state person who has been there for a long time".
"The has been in this fight before, and they have taken aggressive positions to protect that source relationship", said Theresa House, who specializes in First Amendment and media law for Arnold & Portner in NY, told Variety.
The president said it was a "disgrace" the op-ed was published. The department is supposed to make investigative and charging decisions without political interference from the White House.
Trump has openly criticised and ridiculed Sessions for recusing himself from the Russian Federation probe, but the attorney general has embraced Trump's views on most other law enforcement issues, including leaks from inside government.
Trump says if the person had a high-level security clearance, "I don't want him in those meetings".
The party's "central organising principle in foreign policy was the fight against communism and now they're cozying up to the former head of the KGB", he said.
"It is very, very important that whoever released that go to jail, because you can not have members of the intelligence community listening to the most private and highly classified information and then releasing that to The New York Times", Paul said.